require 'set'

class Triplet < Set
  attr_reader :n1, :n2, :n3
  def initialize(n1, n2, n3)
    @n1 = n1
    @n2 = n2
    @n3 = n3
  end

  def sum
    n1 + n2 + n3
  end

  def product
    n1 * n2 * n3
  end

  def pythagorean?
    n1 ** 2 + n2 ** 2 == n3 ** 2
  end

  def self.where(options={})
    max = options[:max_factor]
    min = options[:min_factor] || 1
    sum = options[:sum]
    triplets = []
    (min..max).each do |n1|
      (n1+1..max).each do |n2|
        (n2+1..max).each do |n3|
          set = new(n1, n2, n3)
          if set.pythagorean?
            if sum
              triplets << set if set.sum == sum
            else
              triplets << set
            end
          end
        end
      end
    end
    triplets
  end
end